Shapes can be transformed in a number of ways. These include translation, rotation and reflection. Translation causes a shape to move. Rotation causes a shape to move. Reflection causes a shape to ...

We are fond of saying things are symmetric, but what does that really mean? Intuitively we have a sense of symmetry as a kind of mirroring. Suppose we draw a vertical line through the middle of a ...

A group of mathematicians has shown that at critical moments, a symmetry called rotational invariance is a universal property across many physical systems. For more than 50 years, mathematicians have ...